In the US, it takes 24 business hours to transfer money, sometimes less. Payroll is easy as you know the exact amount and it's on a precise schedule set months in advance.
Additionally, there is at least one person at the company whose full-time job is to handle this. Making a transfer every Tuesday or Wednesday or whatever is well within a workload. When I say "sitting in checking" I quite obviously mean more than two weeks by "sitting".
Also, I was mostly referring to series-A startups that have, for example, single digit millions in the bank. Keeping that all in checking is dumb. Larger companies that are moving millions each week can afford to have special arrangements with their bank or banks to limit liability independent of FDIC. A line of credit, perhaps, that is paid off a week or three later, secured by a bundle of securities held at the same institution, for example. I'm fairly sure a bank run can't touch those.
There are so many possible solutions to this problem.
Maybe it's because I've been burned hard by banks before, but I'll never trust them to not do precisely what SVB did here (in some fashion). Everything's great until it isn't.
EDIT: Engineers making $200k isn't $200k in cash comp, either, FYI. (And anyone with 500 of them has more than one bank account already.)